Question

The following data lists the ages of a random selection of actresses when they won an award in the category of Best​ Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts​ (a) and​ (b) below. Actress left parenthesis years right parenthesisActress (years) 2626 2727 3030 2626 3434 2424 2727 3838 3131 3333 Actor left parenthesis years right parenthesisActor (years) 5959 3434 3333 3939 2929 3434 4747 4040 4040 4343 a. Use the sample data with a 0.050.05 significance level to test the claim that for the population of ages of Best Actresses and Best​ Actors, the differences have a mean less than 0​ (indicating that the Best Actresses are generally younger than Best​ Actors). In this​ example, mu Subscript dμd is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the​ actress's age minus the​ actor's age. What are the null and alternative hypotheses for the hypothesis​ test? Upper H 0H0​: mu Subscript dμd ▼ less than< greater than> not equals≠ equals= nothing ​year(s) Upper H 1H1​: mu Subscript dμd ▼ equals= greater than> not equals≠ less than< nothing ​year(s) ​(Type integers or decimals. Do not​ round.) Identify the test statistic. tequals=nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. ​P-valueequals=nothing ​(Round to three decimal places as​ needed.) What is the conclusion based on the hypothesis​ test? Since the​ P-value is ▼ greater than less than or equal to the significance​ level, ▼ fail to reject reject the null hypothesis. There ▼ is not is sufficient evidence to support the claim that actresses are generally younger when they won the award than actors. b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a). What feature of the confidence interval leads to the same conclusion reached in part​ (a)? The confidence interval is nothing ​year(s)less than

Answer 1

here Ho : ud = 0

H1: ud< 0

since the sample size is less than 30 so we use t test to compute the test sattistic , we have the following outputs from minitab

Two-Sample T-Test and CI: actress, actor

Two-sample T for actress vs actor

N Mean StDev SE Mean
actress 10 29.60 4.40 1.4
actor 10 39.80 8.57 2.7

Difference = μ (actress) - μ (actor)
Estimate for difference: -10.20
95% upper bound for difference: -4.91
T-Test of difference = 0 (vs <): T-Value = -3.35 P-Value = 0.002 DF = 18
Both use Pooled StDev = 6.8150

The test statistic. t = -3.35

p value = 0.002

Since the​ P-value is less than the significance​ level 0.05, reject the null hypothesis. There is not sufficient evidence to support the claim that actresses are generally younger when they won the award than actors.